In this thesis, topological phase realization in photonic crystal and cold atomic gases is discussed. In photonic crystal, we find two pairs of Dirac points can emerge in photonic square lattice. It is further found that these Dirac points originate from the intrinsic mirror symmetry in photonic square lattice. In this way, we establish the relationship between the number of Dirac points and intrinsic mirror symmetry in photonic crystal. When magneto-optical effect is introduced, we claim the realization of photonic Chern insulator with large Chern number, manifesting multiple unidirectional edge states. In cold atomic gases, the realization of 3D Weyl semimetal phase is raised and its corresponding experimental detection scheme is proposed. The Weyl semimetal phase is interpret...[ Read more ]

In this thesis, topological phase realization in photonic crystal and cold atomic gases is discussed. In photonic crystal, we find two pairs of Dirac points can emerge in photonic square lattice. It is further found that these Dirac points originate from the intrinsic mirror symmetry in photonic square lattice. In this way, we establish the relationship between the number of Dirac points and intrinsic mirror symmetry in photonic crystal. When magneto-optical effect is introduced, we claim the realization of photonic Chern insulator with large Chern number, manifesting multiple unidirectional edge states. In cold atomic gases, the realization of 3D Weyl semimetal phase is raised and its corresponding experimental detection scheme is proposed. The Weyl semimetal phase is interpreted as an intermediate state between normal insulator and quantum anomalous Hall insulator. The Landau-Zener transition is developed to measure the signature of the emergence of Weyl points.